LMFDB - Embedded newform 108.5.f.a.19.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(19,108)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.13
Character	$\chi$	$=$	108.19
Dual form			108.5.f.a.91.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.701741 - 3.93796i) q^{2} +(-15.0151 - 5.52686i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(-22.2124 - 12.8243i) q^{7} +(-32.3013 + 55.2506i) q^{8} +O(q^{10})$	\(q+(0.701741 - 3.93796i) q^{2} +(-15.0151 - 5.52686i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(-22.2124 - 12.8243i) q^{7} +(-32.3013 + 55.2506i) q^{8} +(-107.606 + 38.9445i) q^{10} +(93.9677 + 54.2523i) q^{11} +(44.2246 + 76.5993i) q^{13} +(-66.0891 + 78.4722i) q^{14} +(194.908 + 165.973i) q^{16} -504.169 q^{17} +191.405i q^{19} +(77.8502 + 451.079i) q^{20} +(279.585 - 331.970i) q^{22} +(-831.897 + 480.296i) q^{23} +(-96.7443 + 167.566i) q^{25} +(332.680 - 120.402i) q^{26} +(262.643 + 315.324i) q^{28} +(396.671 - 687.053i) q^{29} +(285.428 - 164.792i) q^{31} +(790.370 - 651.069i) q^{32} +(-353.796 + 1985.40i) q^{34} +733.789i q^{35} +209.943 q^{37} +(753.745 + 134.317i) q^{38} +(1830.96 + 9.96965i) q^{40} +(528.200 + 914.869i) q^{41} +(-2887.45 - 1667.07i) q^{43} +(-1111.09 - 1333.95i) q^{44} +(1307.61 + 3613.02i) q^{46} +(-977.185 - 564.178i) q^{47} +(-871.573 - 1509.61i) q^{49} +(591.979 + 498.563i) q^{50} +(-240.684 - 1394.57i) q^{52} -1138.62 q^{53} -3104.23i q^{55} +(1426.04 - 813.005i) q^{56} +(-2427.23 - 2044.21i) q^{58} +(-4037.49 + 2331.05i) q^{59} +(2799.84 - 4849.46i) q^{61} +(-448.648 - 1239.65i) q^{62} +(-2009.25 - 3569.33i) q^{64} +(1265.23 - 2191.45i) q^{65} +(-6127.74 + 3537.85i) q^{67} +(7570.16 + 2786.47i) q^{68} +(2889.63 + 514.930i) q^{70} -4433.42i q^{71} -1953.21 q^{73} +(147.326 - 826.748i) q^{74} +(1057.87 - 2873.97i) q^{76} +(-1391.50 - 2410.15i) q^{77} +(1523.90 + 879.826i) q^{79} +(1324.12 - 7203.27i) q^{80} +(3973.38 - 1438.03i) q^{82} +(2621.64 + 1513.61i) q^{83} +(7211.95 + 12491.5i) q^{85} +(-8591.12 + 10200.8i) q^{86} +(-6032.75 + 3439.35i) q^{88} +559.336 q^{89} -2268.61i q^{91} +(15145.6 - 2613.92i) q^{92} +(-2907.44 + 3452.21i) q^{94} +(4742.31 - 2737.97i) q^{95} +(1100.89 - 1906.79i) q^{97} +(-6556.40 + 2372.87i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	$ 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) $ 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.701741	−	3.93796i	0.175435	−	0.984491i
$2$	0.701741	−	3.93796i	0.175435	−	0.984491i
$3$		0			0
$3$		0			0
$4$	−15.0151	−	5.52686i	−0.938445	−	0.345429i
$5$	−14.3046	−	24.7763i	−0.572185	−	0.991053i	−0.996341	−	0.0854642i	$-0.972763\pi$
$5$	−14.3046	−	24.7763i	−0.572185	−	0.991053i	0.424156	−	0.905589i	$-0.360571\pi$
$6$		0			0
$7$	−22.2124	−	12.8243i	−0.453314	−	0.261721i	0.255915	−	0.966699i	$-0.417623\pi$
$7$	−22.2124	−	12.8243i	−0.453314	−	0.261721i	−0.709229	+	0.704978i	$0.750957\pi$
$8$	−32.3013	+	55.2506i	−0.504708	+	0.863290i
$9$		0			0
$10$	−107.606	+	38.9445i	−1.07606	+	0.389445i
$11$	93.9677	+	54.2523i	0.776593	+	0.448366i	0.835221	−	0.549914i	$-0.185339\pi$
$11$	93.9677	+	54.2523i	0.776593	+	0.448366i	−0.0586287	+	0.998280i	$0.518673\pi$
$12$		0			0
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	0.966690	−	0.255952i	$-0.0823888\pi$
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	−0.705005	+	0.709202i	$0.749055\pi$
$14$	−66.0891	+	78.4722i	−0.337189	+	0.400369i
$15$		0			0
$16$	194.908	+	165.973i	0.761358	+	0.648332i
$17$	−504.169			−1.74453			−0.872265	−	0.489034i	$-0.837349\pi$
$17$	−504.169			−1.74453			−0.872265	+	0.489034i	$0.837349\pi$
$18$		0			0
$19$			191.405i			0.530207i	0.964220	+	0.265104i	$0.0854062\pi$
$19$			191.405i			0.530207i	−0.964220	+	0.265104i	$0.914594\pi$
$20$	77.8502	+	451.079i	0.194625	+	1.12770i
$21$		0			0
$22$	279.585	−	331.970i	0.577654	−	0.685889i
$23$	−831.897	+	480.296i	−1.57258	+	0.907932i	−0.576733	+	0.816933i	$0.695673\pi$
$23$	−831.897	+	480.296i	−1.57258	+	0.907932i	−0.995851	+	0.0909988i	$0.970994\pi$
$24$		0			0
$25$	−96.7443	+	167.566i	−0.154791	+	0.268106i
$26$	332.680	−	120.402i	0.492129	−	0.178110i
$27$		0			0
$28$	262.643	+	315.324i	0.335004	+	0.402199i
$29$	396.671	−	687.053i	0.471665	−	0.816948i	−0.527809	−	0.849363i	$-0.676986\pi$
$29$	396.671	−	687.053i	0.471665	−	0.816948i	0.999475	+	0.0324147i	$0.0103197\pi$
$30$		0			0
$31$	285.428	−	164.792i	0.297011	−	0.171480i	−0.344088	−	0.938937i	$-0.611812\pi$
$31$	285.428	−	164.792i	0.297011	−	0.171480i	0.641099	+	0.767458i	$0.278479\pi$
$32$	790.370	−	651.069i	0.771846	−	0.635809i
$33$		0			0
$34$	−353.796	+	1985.40i	−0.306052	+	1.71747i
$35$			733.789i			0.599011i
$36$		0			0
$37$	209.943			0.153355			0.0766775	−	0.997056i	$-0.475569\pi$
$37$	209.943			0.153355			0.0766775	+	0.997056i	$0.475569\pi$
$38$	753.745	+	134.317i	0.521984	+	0.0930171i
$39$		0			0
$40$	1830.96	+	9.96965i	1.14435	+	0.00623103i
$41$	528.200	+	914.869i	0.314218	+	0.544241i	0.979271	−	0.202555i	$-0.0649245\pi$
$41$	528.200	+	914.869i	0.314218	+	0.544241i	−0.665053	+	0.746796i	$0.731591\pi$
$42$		0			0
$43$	−2887.45	−	1667.07i	−1.56163	−	0.901608i	−0.997093	−	0.0762001i	$-0.975721\pi$
$43$	−2887.45	−	1667.07i	−1.56163	−	0.901608i	−0.564537	−	0.825407i	$-0.690945\pi$
$44$	−1111.09	−	1333.95i	−0.573911	−	0.689024i
$45$		0			0
$46$	1307.61	+	3613.02i	0.617964	+	1.70748i
$47$	−977.185	−	564.178i	−0.442365	−	0.255400i	0.262235	−	0.965004i	$-0.415540\pi$
$47$	−977.185	−	564.178i	−0.442365	−	0.255400i	−0.704600	+	0.709604i	$0.748874\pi$
$48$		0			0
$49$	−871.573	−	1509.61i	−0.363004	−	0.628742i
$50$	591.979	+	498.563i	0.236792	+	0.199425i
$51$		0			0
$52$	−240.684	−	1394.57i	−0.0890104	−	0.515744i
$53$	−1138.62			−0.405346			−0.202673	−	0.979247i	$-0.564963\pi$
$53$	−1138.62			−0.405346			−0.202673	+	0.979247i	$0.564963\pi$
$54$		0			0
$55$		−	3104.23i		−	1.02619i
$56$	1426.04	−	813.005i	0.454732	−	0.259249i
$57$		0			0
$58$	−2427.23	−	2044.21i	−0.721531	−	0.607672i
$59$	−4037.49	+	2331.05i	−1.15987	+	0.669648i	−0.951272	−	0.308354i	$-0.900222\pi$
$59$	−4037.49	+	2331.05i	−1.15987	+	0.669648i	−0.208593	+	0.978002i	$0.566889\pi$
$60$		0			0
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	−0.194193	−	0.980963i	$-0.562209\pi$
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	0.946636	−	0.322305i	$-0.104458\pi$
$62$	−448.648	−	1239.65i	−0.116714	−	0.322488i
$63$		0			0
$64$	−2009.25	−	3569.33i	−0.490540	−	0.871419i
$65$	1265.23	−	2191.45i	0.299463	−	0.518686i
$66$		0			0
$67$	−6127.74	+	3537.85i	−1.36506	+	0.788116i	−0.990292	−	0.139004i	$-0.955610\pi$
$67$	−6127.74	+	3537.85i	−1.36506	+	0.788116i	−0.374764	+	0.927120i	$0.622276\pi$
$68$	7570.16	+	2786.47i	1.63715	+	0.602611i
$69$		0			0
$70$	2889.63	+	514.930i	0.589721	+	0.105088i
$71$		−	4433.42i		−	0.879472i	−0.898127	−	0.439736i	$-0.855072\pi$
$71$		−	4433.42i		−	0.879472i	0.898127	−	0.439736i	$-0.144928\pi$
$72$		0			0
$73$	−1953.21			−0.366524			−0.183262	−	0.983064i	$-0.558666\pi$
$73$	−1953.21			−0.366524			−0.183262	+	0.983064i	$0.558666\pi$
$74$	147.326	−	826.748i	0.0269039	−	0.150977i
$75$		0			0
$76$	1057.87	−	2873.97i	0.183149	−	0.497570i
$77$	−1391.50	−	2410.15i	−0.234694	−	0.406501i
$78$		0			0
$79$	1523.90	+	879.826i	0.244176	+	0.140975i	0.617095	−	0.786889i	$-0.288310\pi$
$79$	1523.90	+	879.826i	0.244176	+	0.140975i	−0.372918	+	0.927864i	$0.621643\pi$
$80$	1324.12	−	7203.27i	0.206894	−	1.12551i
$81$		0			0
$82$	3973.38	−	1438.03i	0.590925	−	0.213865i
$83$	2621.64	+	1513.61i	0.380555	+	0.219714i	0.678060	−	0.735007i	$-0.262821\pi$
$83$	2621.64	+	1513.61i	0.380555	+	0.219714i	−0.297505	+	0.954720i	$0.596154\pi$
$84$		0			0
$85$	7211.95	+	12491.5i	0.998193	+	1.72892i
$86$	−8591.12	+	10200.8i	−1.16159	+	1.37924i
$87$		0			0
$88$	−6032.75	+	3439.35i	−0.779023	+	0.444131i
$89$	559.336			0.0706144			0.0353072	−	0.999377i	$-0.488759\pi$
$89$	559.336			0.0706144			0.0353072	+	0.999377i	$0.488759\pi$
$90$		0			0
$91$		−	2268.61i		−	0.273953i
$92$	15145.6	−	2613.92i	1.78941	−	0.308828i
$93$		0			0
$94$	−2907.44	+	3452.21i	−0.329045	+	0.390698i
$95$	4742.31	−	2737.97i	0.525463	−	0.303376i
$96$		0			0
$97$	1100.89	−	1906.79i	0.117004	−	0.202656i	−0.801575	−	0.597894i	$-0.796004\pi$
$97$	1100.89	−	1906.79i	0.117004	−	0.202656i	0.918579	+	0.395238i	$0.129338\pi$
$98$	−6556.40	+	2372.87i	−0.682674	+	0.247071i
$99$		0			0
$100$	2378.74	−	1981.33i	0.237874	−	0.198133i
$101$	−365.841	+	633.655i	−0.0358632	+	0.0621170i	−0.883400	−	0.468620i	$-0.844751\pi$
$101$	−365.841	+	633.655i	−0.0358632	+	0.0621170i	0.847537	+	0.530737i	$0.178085\pi$
$102$		0			0
$103$	8533.78	−	4926.98i	0.804391	−	0.464415i	−0.0406134	−	0.999175i	$-0.512931\pi$
$103$	8533.78	−	4926.98i	0.804391	−	0.464415i	0.845004	+	0.534760i	$0.179598\pi$
$104$	−5660.67	−	30.8225i	−0.523361	−	0.00284971i
$105$		0			0
$106$	−799.013	+	4483.83i	−0.0711119	+	0.399059i
$107$		−	804.642i		−	0.0702806i	−0.999382	−	0.0351403i	$-0.988812\pi$
$107$		−	804.642i		−	0.0702806i	0.999382	−	0.0351403i	$-0.0111878\pi$
$108$		0			0
$109$	−17324.9			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$109$	−17324.9			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$110$	−12224.4	−	2178.37i	−1.01028	−	0.180030i
$111$		0			0
$112$	−2200.87	−	6186.22i	−0.175452	−	0.493161i
$113$	8573.94	+	14850.5i	0.671465	+	1.16301i	0.977489	+	0.210988i	$0.0676680\pi$
$113$	8573.94	+	14850.5i	0.671465	+	1.16301i	−0.306024	+	0.952024i	$0.598999\pi$
$114$		0			0
$115$	23799.9	+	13740.9i	1.79962	+	1.03901i
$116$	−9753.31	+	8123.85i	−0.724829	+	0.603734i
$117$		0			0
$118$	6346.30	+	17535.3i	0.455782	+	1.25936i
$119$	11198.8	+	6465.63i	0.790820	+	0.456580i
$120$		0			0
$121$	−1433.88	−	2483.55i	−0.0979359	−	0.169630i
$122$	−17132.2	−	14428.7i	−1.15105	−	0.969412i
$123$		0			0
$124$	−5196.51	+	896.848i	−0.337963	+	0.0583278i
$125$	−12345.2			−0.790094
$126$		0			0
$127$			9591.51i			0.594675i	0.954772	+	0.297337i	$0.0960986\pi$
$127$			9591.51i			0.594675i	−0.954772	+	0.297337i	$0.903901\pi$
$128$	−15465.9	+	5407.61i	−0.943962	+	0.330054i
$129$		0			0
$130$	−7741.98	−	6520.27i	−0.458105	−	0.385815i
$131$	3933.27	−	2270.88i	0.229198	−	0.132328i	−0.381004	−	0.924573i	$-0.624422\pi$
$131$	3933.27	−	2270.88i	0.229198	−	0.132328i	0.610202	+	0.792246i	$0.291088\pi$
$132$		0			0
$133$	2454.64	−	4251.56i	0.138766	−	0.240350i
$134$	9631.84	+	26613.5i	0.536414	+	1.48215i
$135$		0			0
$136$	16285.3	−	27855.6i	0.880478	−	1.50604i
$137$	−2450.82	+	4244.95i	−0.130578	+	0.226168i	−0.923900	−	0.382635i	$-0.875017\pi$
$137$	−2450.82	+	4244.95i	−0.130578	+	0.226168i	0.793321	+	0.608803i	$0.208350\pi$
$138$		0			0
$139$	−7491.80	+	4325.39i	−0.387754	+	0.223870i	−0.681187	−	0.732110i	$-0.738536\pi$
$139$	−7491.80	+	4325.39i	−0.387754	+	0.223870i	0.293432	+	0.955980i	$0.405202\pi$
$140$	4055.55	−	11017.9i	0.206916	−	0.562139i
$141$		0			0
$142$	−17458.6	−	3111.11i	−0.865832	−	0.154290i
$143$			9597.15i			0.469321i
$144$		0			0
$145$	−22696.9			−1.07952
$146$	−1370.65	+	7691.66i	−0.0643013	+	0.360840i
$147$		0			0
$148$	−3152.32	−	1160.33i	−0.143915	−	0.0529733i
$149$	−6346.46	−	10992.4i	−0.285863	−	0.495130i	0.686955	−	0.726700i	$-0.258947\pi$
$149$	−6346.46	−	10992.4i	−0.285863	−	0.495130i	−0.972818	+	0.231570i	$0.925614\pi$
$150$		0			0
$151$	11055.3	+	6382.78i	0.484860	+	0.279934i	0.722440	−	0.691434i	$-0.243021\pi$
$151$	11055.3	+	6382.78i	0.484860	+	0.279934i	−0.237579	+	0.971368i	$0.576354\pi$
$152$	−10575.2	−	6182.63i	−0.457723	−	0.267600i
$153$		0			0
$154$	−10467.5	+	3788.37i	−0.441370	+	0.159739i
$155$	−8165.87	−	4714.57i	−0.339891	−	0.196236i
$156$		0			0
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	0.903534	+	0.428516i	$0.140963\pi$
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	−0.0806612	+	0.996742i	$0.525703\pi$
$158$	4534.11	−	5383.67i	0.181626	−	0.215657i
$159$		0			0
$160$	−27437.0	−	10269.2i	−1.07176	−	0.401140i
$161$	24637.9			0.950499
$162$		0			0
$163$		−	6872.98i		−	0.258684i	−0.991600	−	0.129342i	$-0.958713\pi$
$163$		−	6872.98i		−	0.258684i	0.991600	−	0.129342i	$-0.0412865\pi$
$164$	−2874.63	−	16656.2i	−0.106879	−	0.619280i
$165$		0			0
$166$	7800.24	−	9261.78i	0.283069	−	0.336108i
$167$	30405.5	−	17554.6i	1.09023	−	0.629447i	0.156595	−	0.987663i	$-0.449948\pi$
$167$	30405.5	−	17554.6i	1.09023	−	0.629447i	0.933639	+	0.358216i	$0.116615\pi$
$168$		0			0
$169$	10368.9	−	17959.4i	0.363043	−	0.628809i
$170$	54251.8	−	19634.6i	1.87723	−	0.679398i
$171$		0			0
$172$	34141.8	+	40989.9i	1.15406	+	1.38554i
$173$	1491.72	−	2583.74i	0.0498420	−	0.0863290i	−0.840028	−	0.542543i	$-0.817462\pi$
$173$	1491.72	−	2583.74i	0.0498420	−	0.0863290i	0.889870	+	0.456214i	$0.150795\pi$
$174$		0			0
$175$	4297.84	−	2481.36i	0.140338	−	0.0810240i
$176$	9310.60	+	26170.3i	0.300575	+	0.844857i
$177$		0			0
$178$	392.509	−	2202.65i	0.0123883	−	0.0695192i
$179$		−	45199.3i		−	1.41067i	−0.708874	−	0.705335i	$-0.750797\pi$
$179$		−	45199.3i		−	1.41067i	0.708874	−	0.705335i	$-0.249203\pi$
$180$		0			0
$181$	27600.9			0.842492			0.421246	−	0.906946i	$-0.361593\pi$
$181$	27600.9			0.842492			0.421246	+	0.906946i	$0.361593\pi$
$182$	−8933.68	−	1591.97i	−0.269704	−	0.0480610i
$183$		0			0
$184$	334.744	−	61477.0i	0.00988728	−	1.81584i
$185$	−3003.16	−	5201.62i	−0.0877474	−	0.151983i
$186$		0			0
$187$	−47375.6	−	27352.3i	−1.35479	−	0.782188i
$188$	11554.4	+	13872.0i	0.326913	+	0.392484i
$189$		0			0
$190$	−7454.16	−	20596.4i	−0.206487	−	0.570537i
$191$	−16300.9	−	9411.33i	−0.446833	−	0.257979i	0.259659	−	0.965700i	$-0.416390\pi$
$191$	−16300.9	−	9411.33i	−0.446833	−	0.257979i	−0.706492	+	0.707721i	$0.749723\pi$
$192$		0			0
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	0.795571	−	0.605861i	$-0.207171\pi$
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	−0.922476	+	0.386054i	$0.873838\pi$
$194$	−6736.35	−	5673.33i	−0.178987	−	0.150742i
$195$		0			0
$196$	4743.37	+	27484.0i	0.123474	+	0.715432i
$197$	21650.0			0.557860			0.278930	−	0.960311i	$-0.410020\pi$
$197$	21650.0			0.557860			0.278930	+	0.960311i	$0.410020\pi$
$198$		0			0
$199$		−	25261.4i		−	0.637898i	−0.947772	−	0.318949i	$-0.896670\pi$
$199$		−	25261.4i		−	0.637898i	0.947772	−	0.318949i	$-0.103330\pi$
$200$	−6133.15	−	10757.8i	−0.153329	−	0.268944i
$201$		0			0
$202$	2238.58	+	1885.33i	0.0548619	+	0.0462045i
$203$	−17622.0	+	10174.1i	−0.427625	+	0.246889i
$204$		0			0
$205$	15111.4	−	26173.7i	0.359581	−	0.622813i
$206$	−13413.8	−	37063.2i	−0.316094	−	0.873390i
$207$		0			0
$208$	−4093.70	+	22269.9i	−0.0946214	+	0.514744i
$209$	−10384.1	+	17985.9i	−0.237727	+	0.411755i
$210$		0			0
$211$	−18674.0	+	10781.5i	−0.419443	+	0.242166i	−0.694839	−	0.719165i	$-0.744524\pi$
$211$	−18674.0	+	10781.5i	−0.419443	+	0.242166i	0.275396	+	0.961331i	$0.411191\pi$
$212$	17096.4	+	6292.97i	0.380394	+	0.140018i
$213$		0			0
$214$	−3168.65	−	564.650i	−0.0691906	−	0.0123297i
$215$			95387.3i			2.06354i
$216$		0			0
$217$	−8453.38			−0.179519
$218$	−12157.6	+	68224.9i	−0.255821	+	1.43559i
$219$		0			0
$220$	−17156.7	+	46610.4i	−0.354477	+	0.963025i
$221$	−22296.7	−	38619.0i	−0.456516	−	0.790709i
$222$		0			0
$223$	−16709.5	−	9647.22i	−0.336011	−	0.193996i	0.322496	−	0.946571i	$-0.395478\pi$
$223$	−16709.5	−	9647.22i	−0.336011	−	0.193996i	−0.658507	+	0.752575i	$0.728812\pi$
$224$	−25905.5	+	4325.83i	−0.516293	+	0.0862130i
$225$		0			0
$226$	64497.4	−	23342.7i	1.26277	−	0.457018i
$227$	−56144.4	−	32415.0i	−1.08957	−	0.629063i	−0.156107	−	0.987740i	$-0.549895\pi$
$227$	−56144.4	−	32415.0i	−1.08957	−	0.629063i	−0.933462	+	0.358677i	$0.883228\pi$
$228$		0			0
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	0.616784	−	0.787133i	$-0.288435\pi$
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	−0.990069	+	0.140584i	$0.955102\pi$
$230$	70812.6	−	84080.7i	1.33861	−	1.58943i
$231$		0			0
$232$	25147.1	+	44109.0i	0.467210	+	0.819504i
$233$	2307.53			0.0425045			0.0212522	−	0.999774i	$-0.493235\pi$
$233$	2307.53			0.0425045			0.0212522	+	0.999774i	$0.493235\pi$
$234$		0			0
$235$			32281.4i			0.584543i
$236$	73506.8	−	12686.3i	1.31979	−	0.227777i
$237$		0			0
$238$	33320.1	−	39563.3i	0.588237	−	0.698455i
$239$	−65999.7	+	38104.9i	−1.15544	+	0.667091i	−0.950206	−	0.311623i	$-0.899128\pi$
$239$	−65999.7	+	38104.9i	−1.15544	+	0.667091i	−0.205230	+	0.978714i	$0.565794\pi$
$240$		0			0
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	−0.927664	−	0.373416i	$-0.878186\pi$
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	0.787220	+	0.616672i	$0.211520\pi$
$242$	−10786.3	+	3903.75i	−0.184180	+	0.0666579i
$243$		0			0
$244$	−68842.2	+	57340.9i	−1.15631	+	0.963130i
$245$	−24935.0	+	43188.8i	−0.415411	+	0.719513i
$246$		0			0
$247$	−14661.5	+	8464.81i	−0.240317	+	0.138747i
$248$	−114.852	+	21093.0i	−0.00186739	+	0.342954i
$249$		0			0
$250$	−8663.15	+	48615.0i	−0.138610	+	0.777840i
$251$			33833.6i			0.537033i	0.963275	+	0.268517i	$0.0865334\pi$
$251$			33833.6i			0.537033i	−0.963275	+	0.268517i	$0.913467\pi$
$252$		0			0
$253$	−104229.			−1.62834
$254$	37771.0	+	6730.76i	0.585452	+	0.104327i
$255$		0			0
$256$	10441.9	+	64698.8i	0.159331	+	0.987225i
$257$	−28773.1	−	49836.4i	−0.435632	−	0.754537i	0.561715	−	0.827331i	$-0.310142\pi$
$257$	−28773.1	−	49836.4i	−0.435632	−	0.754537i	−0.997347	+	0.0727940i	$0.976808\pi$
$258$		0			0
$259$	−4663.34	−	2692.38i	−0.0695180	−	0.0401362i
$260$	−31109.5	+	25912.1i	−0.460199	+	0.383315i
$261$		0			0
$262$	−6182.49	−	17082.6i	−0.0900659	−	0.248859i
$263$	68019.2	+	39270.9i	0.983378	+	0.567753i	0.903288	−	0.429034i	$-0.141146\pi$
$263$	68019.2	+	39270.9i	0.983378	+	0.567753i	0.0800895	+	0.996788i	$0.474479\pi$
$264$		0			0
$265$	16287.5	+	28210.7i	0.231933	+	0.401719i
$266$	−15020.0	−	12649.8i	−0.212278	−	0.178780i
$267$		0			0
$268$	111562.	−	19254.1i	1.55327	−	0.268073i
$269$	5376.96			0.0743074			0.0371537	−	0.999310i	$-0.488171\pi$
$269$	5376.96			0.0743074			0.0371537	+	0.999310i	$0.488171\pi$
$270$		0			0
$271$		−	108113.i		−	1.47211i	−0.676924	−	0.736053i	$-0.736688\pi$
$271$		−	108113.i		−	1.47211i	0.676924	−	0.736053i	$-0.263312\pi$
$272$	−98266.4	−	83678.5i	−1.32821	−	1.13103i
$273$		0			0
$274$	14996.6	+	12630.1i	0.199752	+	0.168231i
$275$	−18181.7	+	10497.2i	−0.240419	+	0.138806i
$276$		0			0
$277$	21971.1	−	38055.1i	0.286347	−	0.495968i	−0.686588	−	0.727047i	$-0.740892\pi$
$277$	21971.1	−	38055.1i	0.286347	−	0.495968i	0.972935	+	0.231079i	$0.0742255\pi$
$278$	11775.9	+	32537.8i	0.152372	+	0.421015i
$279$		0			0
$280$	−40542.2	−	23702.3i	−0.517120	−	0.302326i
$281$	25435.7	−	44055.9i	0.322130	−	0.557945i	−0.658798	−	0.752320i	$-0.728935\pi$
$281$	25435.7	−	44055.9i	0.322130	−	0.557945i	0.980927	+	0.194375i	$0.0622680\pi$
$282$		0			0
$283$	−22858.8	+	13197.5i	−0.285418	+	0.164786i	−0.635873	−	0.771793i	$-0.719360\pi$
$283$	−22858.8	+	13197.5i	−0.285418	+	0.164786i	0.350456	+	0.936579i	$0.386027\pi$
$284$	−24502.9	+	66568.3i	−0.303795	+	0.825336i
$285$		0			0
$286$	37793.2	+	6734.71i	0.462042	+	0.0823355i
$287$		−	27095.2i		−	0.328950i
$288$		0			0
$289$	170665.			2.04338
$290$	−15927.3	+	89379.5i	−0.189386	+	1.06278i
$291$		0			0
$292$	29327.6	+	10795.1i	0.343963	+	0.126608i
$293$	65395.3	+	113268.i	0.761748	+	1.31939i	0.941949	+	0.335757i	$0.108992\pi$
$293$	65395.3	+	113268.i	0.761748	+	1.31939i	−0.180201	+	0.983630i	$0.557675\pi$
$294$		0			0
$295$	115510.	+	66689.5i	1.32731	+	0.766325i
$296$	−6781.44	+	11599.5i	−0.0773995	+	0.132390i
$297$		0			0
$298$	−47741.2	+	17278.3i	−0.537602	+	0.194567i
$299$	−73580.7	−	42481.8i	−0.823041	−	0.475183i
$300$		0			0
$301$	42758.2	+	74059.3i	0.471939	+	0.817423i
$302$	32893.1	−	39056.3i	0.360654	−	0.428230i
$303$		0			0
$304$	−31768.0	+	37306.2i	−0.343750	+	0.403677i
$305$	−160202.			−1.72214
$306$		0			0
$307$			54227.3i			0.575362i	0.957726	+	0.287681i	$0.0928843\pi$
$307$			54227.3i			0.575362i	−0.957726	+	0.287681i	$0.907116\pi$
$308$	7572.97	+	43879.3i	0.0798297	+	0.462549i
$309$		0			0
$310$	−24296.1	+	28848.5i	−0.252821	+	0.300193i
$311$	117745.	−	67980.1i	1.21737	−	0.702847i	0.253013	−	0.967463i	$-0.418578\pi$
$311$	117745.	−	67980.1i	1.21737	−	0.702847i	0.964354	+	0.264616i	$0.0852451\pi$
$312$		0			0
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	0.0517658	+	0.998659i	$0.483515\pi$
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	−0.890747	+	0.454499i	$0.849818\pi$
$314$	152579.	−	55220.7i	1.54751	−	0.560070i
$315$		0			0
$316$	−18018.9	−	21633.1i	−0.180449	−	0.216643i
$317$	60309.5	−	104459.i	0.600160	−	1.03951i	−0.392637	−	0.919694i	$-0.628437\pi$
$317$	60309.5	−	104459.i	0.600160	−	1.03951i	0.992796	−	0.119814i	$-0.0382297\pi$
$318$		0			0
$319$	74548.4	−	43040.6i	0.732584	−	0.422957i
$320$	−59693.4	+	100840.i	−0.582943	+	0.984763i
$321$		0			0
$322$	17289.4	−	97023.1i	0.166751	−	0.935758i
$323$		−	96500.4i		−	0.924962i
$324$		0			0
$325$	−17113.9			−0.162025
$326$	−27065.5	−	4823.05i	−0.254672	−	0.0453823i
$327$		0			0
$328$	−67608.6	−	368.131i	−0.628426	−	0.00342180i
$329$	14470.4	+	25063.5i	0.133687	+	0.231553i
$330$		0			0
$331$	−100184.	−	57841.2i	−0.914412	−	0.527936i	−0.0325639	−	0.999470i	$-0.510367\pi$
$331$	−100184.	−	57841.2i	−0.914412	−	0.527936i	−0.881848	+	0.471534i	$0.843701\pi$
$332$	−30998.8	−	37216.5i	−0.281235	−	0.337644i
$333$		0			0
$334$	−47792.7	−	132055.i	−0.428419	−	1.18375i
$335$	175310.	+	101215.i	1.56213	+	0.901895i
$336$		0			0
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	−0.900746	−	0.434347i	$-0.856979\pi$
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	0.0742175	−	0.997242i	$-0.476354\pi$
$338$	−63447.2	−	53435.1i	−0.555366	−	0.467728i
$339$		0			0
$340$	−39249.7	−	227420.i	−0.339530	−	1.96730i
$341$	35761.3			0.307542
$342$		0			0
$343$			106292.i			0.903465i
$344$	185375.	−	105685.i	1.56652	−	0.893091i
$345$		0			0
$346$	−9127.87	−	7687.47i	−0.0762460	−	0.0642142i
$347$	−117124.	+	67621.8i	−0.972721	+	0.561601i	−0.900065	−	0.435756i	$-0.856481\pi$
$347$	−117124.	+	67621.8i	−0.972721	+	0.561601i	−0.0726566	+	0.997357i	$0.523148\pi$
$348$		0			0
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	−0.872725	−	0.488212i	$-0.837649\pi$
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	0.859167	+	0.511696i	$0.170983\pi$
$350$	−6755.54	−	18666.0i	−0.0551472	−	0.152376i
$351$		0			0
$352$	109591.	−	18300.1i	0.884485	−	0.147695i
$353$	21366.4	−	37007.7i	0.171467	−	0.296990i	−0.767466	−	0.641090i	$-0.778483\pi$
$353$	21366.4	−	37007.7i	0.171467	−	0.296990i	0.938933	+	0.344100i	$0.111816\pi$
$354$		0			0
$355$	−109844.	+	63418.4i	−0.871603	+	0.503220i
$356$	−8398.50	−	3091.38i	−0.0662677	−	0.0243922i
$357$		0			0
$358$	−177993.	−	31718.2i	−1.38879	−	0.247481i
$359$		−	175816.i		−	1.36418i	−0.731270	−	0.682088i	$-0.761072\pi$
$359$		−	175816.i		−	1.36418i	0.731270	−	0.682088i	$-0.238928\pi$
$360$		0			0
$361$	93685.2			0.718880
$362$	19368.7	−	108691.i	0.147803	−	0.829426i
$363$		0			0
$364$	−12538.3	+	34063.4i	−0.0946313	+	0.257090i
$365$	27939.9	+	48393.3i	0.209719	+	0.363245i
$366$		0			0
$367$	−6867.31	−	3964.84i	−0.0509864	−	0.0294370i	0.474290	−	0.880369i	$-0.342705\pi$
$367$	−6867.31	−	3964.84i	−0.0509864	−	0.0294370i	−0.525277	+	0.850932i	$0.676038\pi$
$368$	−241859.	−	44459.1i	−1.78594	−	0.328296i
$369$		0			0
$370$	−22591.2	+	8176.13i	−0.165020	+	0.0597234i
$371$	25291.4	+	14602.0i	0.183749	+	0.106087i
$372$		0			0
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.844001	−	0.536342i	$-0.819806\pi$
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.0424851	−	0.999097i	$-0.513527\pi$
$374$	−140958.	+	167369.i	−1.00773	+	1.19655i
$375$		0			0
$376$	62735.5	−	35766.3i	0.443749	−	0.252987i
$377$	70170.4			0.493709
$378$		0			0
$379$			147423.i			1.02633i	0.858291	+	0.513163i	$0.171526\pi$
$379$			147423.i			1.02633i	−0.858291	+	0.513163i	$0.828474\pi$
$380$	−86338.7	+	14900.9i	−0.597914	+	0.103192i
$381$		0			0
$382$	−48500.5	+	57588.0i	−0.332368	+	0.394644i
$383$	105968.	−	61180.9i	0.722402	−	0.417079i	−0.0932341	−	0.995644i	$-0.529720\pi$
$383$	105968.	−	61180.9i	0.722402	−	0.417079i	0.815636	+	0.578565i	$0.196387\pi$
$384$		0			0
$385$	−39809.7	+	68952.5i	−0.268576	+	0.465188i
$386$	−35559.6	+	12869.6i	−0.238662	+	0.0863755i
$387$		0			0
$388$	−27068.6	+	22546.3i	−0.179805	+	0.149765i
$389$	−91728.1	+	158878.i	−0.606182	+	1.04994i	0.385682	+	0.922632i	$0.373966\pi$
$389$	−91728.1	+	158878.i	−0.606182	+	1.04994i	−0.991863	+	0.127306i	$0.959367\pi$
$390$		0			0
$391$	419417.	−	242150.i	2.74342	−	1.58391i
$392$	111560.	+	607.446i	0.725998	+	0.00395308i
$393$		0			0
$394$	15192.7	−	85256.9i	0.0978684	−	0.549208i
$395$		−	50342.3i		−	0.322656i
$396$		0			0
$397$	81466.1			0.516887			0.258444	−	0.966026i	$-0.416790\pi$
$397$	81466.1			0.516887			0.258444	+	0.966026i	$0.416790\pi$
$398$	−99478.5	−	17727.0i	−0.628005	−	0.111910i
$399$		0			0
$400$	−46667.6	+	16602.9i	−0.291673	+	0.103768i
$401$	100584.	+	174217.i	0.625518	+	1.08343i	0.988440	+	0.151610i	$0.0484459\pi$
$401$	100584.	+	174217.i	0.625518	+	1.08343i	−0.362922	+	0.931820i	$0.618221\pi$
$402$		0			0
$403$	25245.9	+	14575.7i	0.155446	+	0.0897469i
$404$	8995.27	−	7492.45i	0.0551127	−	0.0459051i
$405$		0			0
$406$	27699.0	+	76534.4i	0.168040	+	0.464306i
$407$	19727.9	+	11389.9i	0.119094	+	0.0687592i
$408$		0			0
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	0.995976	−	0.0896241i	$-0.0285666\pi$
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	−0.575605	+	0.817728i	$0.695233\pi$
$410$	−92466.8	−	77875.3i	−0.550070	−	0.463268i
$411$		0			0
$412$	−155367.	+	26814.2i	−0.915299	+	0.157968i
$413$	119576.			0.701044
$414$		0			0
$415$		−	86606.3i		−	0.502867i
$416$	84825.3	+	31748.5i	0.490161	+	0.183458i
$417$		0			0
$418$	63540.7	+	53513.8i	0.363663	+	0.306276i
$419$	133102.	−	76846.6i	0.758154	−	0.437720i	−0.0704785	−	0.997513i	$-0.522453\pi$
$419$	133102.	−	76846.6i	0.758154	−	0.437720i	0.828633	+	0.559793i	$0.189119\pi$
$420$		0			0
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	−0.997344	−	0.0728309i	$-0.976797\pi$
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	0.561746	+	0.827310i	$0.310130\pi$
$422$	29352.6	+	81103.5i	0.164825	+	0.455422i
$423$		0			0
$424$	36778.8	−	62909.2i	0.204581	−	0.349931i
$425$	48775.5	−	84481.6i	0.270037	−	0.467718i
$426$		0			0
$427$	−124382.	+	71812.1i	−0.682186	+	0.393860i
$428$	−4447.15	+	12081.8i	−0.0242769	+	0.0659544i
$429$		0			0
$430$	375632.	+	66937.2i	2.03154	+	0.362019i
$431$			191579.i			1.03132i	0.856793	+	0.515660i	$0.172453\pi$
$431$			191579.i			1.03132i	−0.856793	+	0.515660i	$0.827547\pi$
$432$		0			0
$433$	−53963.8			−0.287824			−0.143912	−	0.989591i	$-0.545968\pi$
$433$	−53963.8			−0.287824			−0.143912	+	0.989591i	$0.545968\pi$
$434$	−5932.08	+	33289.1i	−0.0314940	+	0.176735i
$435$		0			0
$436$	260136.	+	95752.5i	1.36844	+	0.503706i
$437$	−91930.9	−	159229.i	−0.481392	−	0.833795i
$438$		0			0
$439$	14586.4	+	8421.44i	0.0756864	+	0.0436976i	0.537366	−	0.843349i	$-0.319420\pi$
$439$	14586.4	+	8421.44i	0.0756864	+	0.0436976i	−0.461679	+	0.887047i	$0.652753\pi$
$440$	171511.	+	100271.i	0.885902	+	0.517928i
$441$		0			0
$442$	−167727.	+	60703.0i	−0.858534	+	0.310718i
$443$	−140111.	−	80892.9i	−0.713943	−	0.412195i	0.0985761	−	0.995130i	$-0.468571\pi$
$443$	−140111.	−	80892.9i	−0.713943	−	0.412195i	−0.812519	+	0.582934i	$0.801905\pi$
$444$		0			0
$445$	−8001.09	−	13858.3i	−0.0404045	−	0.0699826i
$446$	−49716.1	+	59031.5i	−0.249935	+	0.296766i
$447$		0			0
$448$	−1144.04	+	105051.i	−0.00570015	+	0.523411i
$449$	−127200.			−0.630949			−0.315475	−	0.948934i	$-0.602164\pi$
$449$	−127200.			−0.630949			−0.315475	+	0.948934i	$0.602164\pi$
$450$		0			0
$451$			114624.i			0.563538i
$452$	−46662.0	−	270369.i	−0.228395	−	1.32337i
$453$		0			0
$454$	−167048.	+	198348.i	−0.810456	+	0.962311i
$455$	−56207.7	+	32451.5i	−0.271502	+	0.156752i
$456$		0			0
$457$	9423.93	−	16322.7i	0.0451232	−	0.0781556i	−0.842582	−	0.538569i	$-0.818965\pi$
$457$	9423.93	−	16322.7i	0.0451232	−	0.0781556i	0.887705	+	0.460413i	$0.152299\pi$
$458$	−147256.	+	53294.4i	−0.702009	+	0.254068i
$459$		0			0
$460$	−281415.	−	337860.i	−1.32994	−	1.59669i
$461$	−29335.9	+	50811.3i	−0.138038	+	0.239088i	−0.926754	−	0.375669i	$-0.877413\pi$
$461$	−29335.9	+	50811.3i	−0.138038	+	0.239088i	0.788716	+	0.614758i	$0.210746\pi$
$462$		0			0
$463$	−41167.7	+	23768.2i	−0.192041	+	0.110875i	−0.592938	−	0.805248i	$-0.702032\pi$
$463$	−41167.7	+	23768.2i	−0.192041	+	0.110875i	0.400897	+	0.916123i	$0.368699\pi$
$464$	191346.	−	68075.3i	0.888760	−	0.316194i
$465$		0			0
$466$	1619.29	−	9086.96i	0.00745679	−	0.0418453i
$467$			150686.i			0.690936i	0.938431	+	0.345468i	$0.112280\pi$
$467$			150686.i			0.690936i	−0.938431	+	0.345468i	$0.887720\pi$
$468$		0			0
$469$	181482.			0.825066
$470$	127123.	+	22653.2i	0.575478	+	0.102550i
$471$		0			0
$472$	1624.63	−	298370.i	0.00729240	−	1.33928i
$473$	−180885.	−	313302.i	−0.808500	−	1.40036i
$474$		0			0
$475$	−32072.9	−	18517.3i	−0.142152	−	0.0820712i
$476$	−132417.	−	158976.i	−0.584425	−	0.701647i
$477$		0			0
$478$	103741.	+	286644.i	0.454041	+	1.25455i
$479$	47830.3	+	27614.8i	0.208464	+	0.120357i	0.600598	−	0.799551i	$-0.294929\pi$
$479$	47830.3	+	27614.8i	0.208464	+	0.120357i	−0.392133	+	0.919908i	$0.628263\pi$
$480$		0			0
$481$	9284.65	+	16081.5i	0.0401306	+	0.0695082i
$482$	49913.5	+	42037.0i	0.214844	+	0.180941i
$483$		0			0
$484$	7803.61	+	45215.7i	0.0333123	+	0.193018i
$485$	−62991.1			−0.267791
$486$		0			0
$487$		−	2975.59i		−	0.0125463i	−0.999980	−	0.00627313i	$-0.998003\pi$
$487$		−	2975.59i		−	0.0125463i	0.999980	−	0.00627313i	$-0.00199681\pi$
$488$	177497.	+	311337.i	0.745335	+	1.30735i
$489$		0			0
$490$	152578.	+	128501.i	0.635476	+	0.535196i
$491$	−234443.	+	135356.i	−0.972467	+	0.561454i	−0.899987	−	0.435916i	$-0.856424\pi$
$491$	−234443.	+	135356.i	−0.972467	+	0.561454i	−0.0724794	+	0.997370i	$0.523091\pi$
$492$		0			0
$493$	−199989.	+	346391.i	−0.822834	+	1.42519i
$494$	23045.5	+	63676.5i	0.0944350	+	0.260931i
$495$		0			0
$496$	82983.0	+	15254.1i	0.337307	+	0.0620047i
$497$	−56855.6	+	98476.8i	−0.230176	+	0.398677i
$498$		0			0
$499$	−226339.	+	130677.i	−0.908988	+	0.524805i	−0.880105	−	0.474778i	$-0.842528\pi$
$499$	−226339.	+	130677.i	−0.908988	+	0.524805i	−0.0288827	+	0.999583i	$0.509195\pi$
$500$	185365.	+	68230.3i	0.741459	+	0.272921i
$501$		0			0
$502$	133236.	+	23742.5i	0.528704	+	0.0942146i
$503$			283008.i			1.11857i	0.828976	+	0.559284i	$0.188924\pi$
$503$			283008.i			1.11857i	−0.828976	+	0.559284i	$0.811076\pi$
$504$		0			0
$505$	20932.9			0.0820816
$506$	−73141.5	+	410448.i	−0.285669	+	1.60309i
$507$		0			0
$508$	53010.9	−	144018.i	0.205418	−	0.558069i
$509$	−106839.	−	185051.i	−0.412378	−	0.714259i	0.582772	−	0.812636i	$-0.301968\pi$
$509$	−106839.	−	185051.i	−0.412378	−	0.714259i	−0.995149	+	0.0983769i	$0.968635\pi$
$510$		0			0
$511$	43385.4	+	25048.6i	0.166151	+	0.0959271i
$512$	262109.	+	4281.91i	0.999867	+	0.0163342i
$513$		0			0
$514$	−216445.	+	78335.0i	−0.819260	+	0.296503i
$515$	−244145.	−	140957.i	−0.920520	−	0.531463i
$516$		0			0
$517$	−61215.9	−	106029.i	−0.229025	−	0.396683i
$518$	−13874.9	+	16474.7i	−0.0517097	+	0.0613985i
$519$		0			0
$520$	80210.0	+	140691.i	0.296635	+	0.520309i
$521$	−168525.			−0.620854			−0.310427	−	0.950597i	$-0.600472\pi$
$521$	−168525.			−0.620854			−0.310427	+	0.950597i	$0.600472\pi$
$522$		0			0
$523$		−	231592.i		−	0.846681i	−0.905971	−	0.423340i	$-0.860857\pi$
$523$		−	231592.i		−	0.846681i	0.905971	−	0.423340i	$-0.139143\pi$
$524$	−71609.4	+	12358.8i	−0.260800	+	0.0450105i
$525$		0			0
$526$	202379.	−	240299.i	0.731467	−	0.868522i
$527$	−143904.	+	83082.9i	−0.518145	+	0.299151i
$528$		0			0
$529$	321448.	−	556764.i	1.14868	−	1.98957i
$530$	122522.	−	44342.8i	0.436178	−	0.157860i
$531$		0			0
$532$	−60354.5	+	50271.2i	−0.213249	+	0.177622i
$533$	−46718.9	+	80919.5i	−0.164452	+	0.284839i
$534$		0			0
$535$	−19936.1	+	11510.1i	−0.0696518	+	0.0402135i
$536$	2465.72	−	452838.i	0.00858250	−	1.57621i
$537$		0			0
$538$	3773.23	−	21174.3i	0.0130361	−	0.0731550i
$539$		−	189139.i		−	0.651035i
$540$		0			0
$541$	−3552.06			−0.0121363			−0.00606815	−	0.999982i	$-0.501932\pi$
$541$	−3552.06			−0.0121363			−0.00606815	+	0.999982i	$0.501932\pi$
$542$	−425745.	−	75867.3i	−1.44927	−	0.258259i
$543$		0			0
$544$	−398480.	+	328249.i	−1.34651	+	1.10919i
$545$	247826.	+	429248.i	0.834362	+	1.44516i
$546$		0			0
$547$	−444293.	−	256513.i	−1.48489	−	0.857302i	−0.485039	−	0.874493i	$-0.661195\pi$
$547$	−444293.	−	256513.i	−1.48489	−	0.857302i	−0.999852	+	0.0171904i	$0.994528\pi$
$548$	60260.6	−	50193.0i	0.200665	−	0.167141i
$549$		0			0
$550$	28578.7	+	78965.1i	0.0944752	+	0.261042i
$551$	131505.	+	75924.6i	0.433152	+	0.250080i
$552$		0			0
$553$	−22566.4	−	39086.1i	−0.0737924	−	0.127812i
$554$	−134442.	−	113226.i	−0.438041	−	0.368917i
$555$		0			0
$556$	136396.	−	23540.1i	0.441217	−	0.0761482i
$557$	269383.			0.868281			0.434141	−	0.900845i	$-0.357052\pi$
$557$	269383.			0.868281			0.434141	+	0.900845i	$0.357052\pi$
$558$		0			0
$559$		−	294903.i		−	0.943746i
$560$	−121789.	+	143021.i	−0.388358	+	0.456062i
$561$		0			0
$562$	−155641.	−	131081.i	−0.492779	−	0.415017i
$563$	48439.2	−	27966.4i	0.152820	−	0.0882307i	−0.421640	−	0.906763i	$-0.638545\pi$
$563$	48439.2	−	27966.4i	0.152820	−	0.0882307i	0.574460	+	0.818533i	$0.305212\pi$
$564$		0			0
$565$	245294.	−	424861.i	0.768404	−	1.33092i
$566$	35930.5	+	99278.4i	0.112158	+	0.309900i
$567$		0			0
$568$	244949.	+	143205.i	0.759239	+	0.443877i
$569$	212266.	−	367655.i	0.655625	−	1.13558i	−0.326111	−	0.945331i	$-0.605738\pi$
$569$	212266.	−	367655.i	0.655625	−	1.13558i	0.981737	−	0.190245i	$-0.0609282\pi$
$570$		0			0
$571$	−25297.4	+	14605.5i	−0.0775897	+	0.0447964i	−0.538293	−	0.842758i	$-0.680931\pi$
$571$	−25297.4	+	14605.5i	−0.0775897	+	0.0447964i	0.460703	+	0.887554i	$0.347597\pi$
$572$	53042.1	−	144102.i	0.162117	−	0.440432i
$573$		0			0
$574$	−106700.	−	19013.9i	−0.323848	−	0.0577094i
$575$		−	185863.i		−	0.562158i
$576$		0			0
$577$	−494524.			−1.48537			−0.742687	−	0.669639i	$-0.766449\pi$
$577$	−494524.			−1.48537			−0.742687	+	0.669639i	$0.766449\pi$
$578$	119763.	−	672074.i	0.358482	−	2.01169i
$579$		0			0
$580$	340796.	+	125443.i	1.01307	+	0.372897i
$581$	−38822.0	−	67241.7i	−0.115007	−	0.199199i
$582$		0			0
$583$	−106993.	−	61772.5i	−0.314788	−	0.181743i
$584$	63091.1	−	107916.i	0.184988	−	0.316417i
$585$		0			0
$586$	491936.	−	178040.i	1.43256	−	0.518467i
$587$	−208206.	−	120208.i	−0.604251	−	0.348865i	0.166461	−	0.986048i	$-0.446766\pi$
$587$	−208206.	−	120208.i	−0.604251	−	0.348865i	−0.770712	+	0.637183i	$0.780099\pi$
$588$		0			0
$589$	31541.9	+	54632.2i	0.0909197	+	0.157477i
$590$	343678.	−	408074.i	0.987298	−	1.17229i
$591$		0			0
$592$	40919.5	+	34844.9i	0.116758	+	0.0994250i
$593$	470902.			1.33912			0.669562	−	0.742756i	$-0.266482\pi$
$593$	470902.			1.33912			0.669562	+	0.742756i	$0.266482\pi$
$594$		0			0
$595$		−	369954.i		−	1.04499i
$596$	34539.4	+	200128.i	0.0972349	+	0.563398i
$597$		0			0
$598$	−218926.	+	259947.i	−0.612203	+	0.726912i
$599$	8669.92	−	5005.58i	0.0241636	−	0.0139509i	−0.487870	−	0.872917i	$-0.662226\pi$
$599$	8669.92	−	5005.58i	0.0241636	−	0.0139509i	0.512033	+	0.858966i	$0.328892\pi$
$600$		0			0
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	0.454800	+	0.890593i	$0.349711\pi$
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	−0.998677	+	0.0514280i	$0.983623\pi$
$602$	321648.	−	116410.i	0.887540	−	0.321215i
$603$		0			0
$604$	−130720.	−	156939.i	−0.358317	−	0.430188i
$605$	−41022.2	+	71052.5i	−0.112075	+	0.194119i
$606$		0			0
$607$	−375426.	+	216752.i	−1.01894	+	0.588283i	−0.913796	−	0.406174i	$-0.866863\pi$
$607$	−375426.	+	216752.i	−1.01894	+	0.588283i	−0.105141	+	0.994457i	$0.533529\pi$
$608$	124618.	+	151281.i	0.337111	+	0.409238i
$609$		0			0
$610$	−112421.	+	630872.i	−0.302125	+	1.69544i
$611$		−	99802.2i		−	0.267336i
$612$		0			0
$613$	301951.			0.803555			0.401778	−	0.915737i	$-0.368393\pi$
$613$	301951.			0.803555			0.401778	+	0.915737i	$0.368393\pi$
$614$	213545.	+	38053.5i	0.566439	+	0.100939i
$615$		0			0
$616$	178109.	+	969.810i	0.469380	+	0.00255579i
$617$	98373.3	+	170388.i	0.258409	+	0.447577i	0.965816	−	0.259229i	$-0.0834686\pi$
$617$	98373.3	+	170388.i	0.258409	+	0.447577i	−0.707407	+	0.706806i	$0.750135\pi$
$618$		0			0
$619$	536199.	+	309575.i	1.39941	+	0.807949i	0.994331	−	0.106333i	$-0.0339110\pi$
$619$	536199.	+	309575.i	1.39941	+	0.807949i	0.405078	+	0.914282i	$0.367244\pi$
$620$	96554.8	+	115921.i	0.251183	+	0.301565i
$621$		0			0
$622$	−185077.	−	511380.i	−0.478378	−	1.32179i
$623$	−12424.2	−	7173.12i	−0.0320105	−	0.0184813i
$624$		0			0
$625$	237059.	+	410598.i	0.606870	+	1.05113i
$626$	502947.	+	423581.i	1.28343	+	1.08090i
$627$		0			0
$628$	−110386.	−	639600.i	−0.279896	−	1.62177i
$629$	−105847.			−0.267532
$630$		0			0
$631$			308766.i			0.775479i	0.921769	+	0.387740i	$0.126744\pi$
$631$			308766.i			0.775479i	−0.921769	+	0.387740i	$0.873256\pi$
$632$	−97835.0	+	55777.0i	−0.244940	+	0.139644i
$633$		0			0
$634$	−369034.	−	310800.i	−0.918096	−	0.773218i
$635$	237642.	−	137203.i	0.589354	−	0.340264i
$636$		0			0
$637$	77090.0	−	133524.i	0.189985	−	0.329064i
$638$	−117178.	−	323772.i	−0.287877	−	0.795424i
$639$		0			0
$640$	355214.	+	305834.i	0.867222	+	0.746665i
$641$	−171200.	+	296528.i	−0.416666	+	0.721687i	−0.995602	−	0.0936860i	$-0.970135\pi$
$641$	−171200.	+	296528.i	−0.416666	+	0.721687i	0.578935	+	0.815373i	$0.303468\pi$
$642$		0			0
$643$	478867.	−	276474.i	1.15823	−	0.668702i	0.207347	−	0.978267i	$-0.433517\pi$
$643$	478867.	−	276474.i	1.15823	−	0.668702i	0.950878	+	0.309566i	$0.100184\pi$
$644$	−369941.	−	136170.i	−0.891991	−	0.328330i
$645$		0			0
$646$	−380015.	−	67718.3i	−0.910617	−	0.162271i
$647$			576814.i			1.37793i	0.724794	+	0.688965i	$0.241935\pi$
$647$			576814.i			1.37793i	−0.724794	+	0.688965i	$0.758065\pi$
$648$		0			0
$649$	−505858.			−1.20099
$650$	−12009.5	+	67394.0i	−0.0284250	+	0.159512i
$651$		0			0
$652$	−37986.0	+	103199.i	−0.0893569	+	0.242761i
$653$	−286795.	−	496744.i	−0.672583	−	1.16495i	−0.977169	−	0.212463i	$-0.931852\pi$
$653$	−286795.	−	496744.i	−0.672583	−	1.16495i	0.304586	−	0.952485i	$-0.401482\pi$
$654$		0			0
$655$	−112528.	−	64968.0i	−0.262288	−	0.151432i
$656$	−48893.4	+	265982.i	−0.113617	+	0.618080i
$657$		0			0
$658$	108854.	−	39395.9i	0.251415	−	0.0909911i
$659$	−299298.	−	172800.i	−0.689180	−	0.397899i	0.114125	−	0.993466i	$-0.463594\pi$
$659$	−299298.	−	172800.i	−0.689180	−	0.397899i	−0.803305	+	0.595568i	$0.796927\pi$
$660$		0			0
$661$	187583.	+	324904.i	0.429330	+	0.743622i	0.996814	−	0.0797628i	$-0.0254163\pi$
$661$	187583.	+	324904.i	0.429330	+	0.743622i	−0.567484	+	0.823385i	$0.692083\pi$
$662$	−298080.	+	353931.i	−0.680168	+	0.807612i
$663$		0			0
$664$	−168310.	+	95955.8i	−0.381746	+	0.217638i
$665$	−140451.			−0.317600
$666$		0			0
$667$			762077.i			1.71296i
$668$	−553565.	+	95537.8i	−1.24055	+	0.214103i
$669$		0			0
$670$	521604.	−	619337.i	1.16196	−	1.37968i
$671$	526189.	−	303795.i	1.16868	−	0.674739i
$672$		0			0
$673$	286866.	−	496866.i	0.633358	−	1.09701i	−0.353503	−	0.935433i	$-0.615010\pi$
$673$	286866.	−	496866.i	0.633358	−	1.09701i	0.986861	−	0.161574i	$-0.0516571\pi$
$674$	−706121.	+	255557.i	−1.55439	+	0.562558i
$675$		0			0
$676$	−254949.	+	212355.i	−0.557904	+	0.464697i
$677$	−13789.2	+	23883.6i	−0.0300859	+	0.0521103i	−0.880676	−	0.473719i	$-0.842911\pi$
$677$	−13789.2	+	23883.6i	−0.0300859	+	0.0521103i	0.850590	+	0.525829i	$0.176245\pi$
$678$		0			0
$679$	−48906.7	+	28236.3i	−0.106079	+	0.0612447i
$680$	−923116.	−	5026.39i	−1.99636	−	0.0108702i
$681$		0			0
$682$	25095.2	−	140827.i	0.0539538	−	0.302773i
$683$		−	1038.30i		−	0.00222578i	−0.999999	−	0.00111289i	$-0.999646\pi$
$683$		−	1038.30i		−	0.00222578i	0.999999	−	0.00111289i	$-0.000354244\pi$
$684$		0			0
$685$	140232.			0.298859
$686$	418573.	+	74589.3i	0.889454	+	0.158500i
$687$		0			0
$688$	−286098.	−	804164.i	−0.604418	−	1.69890i
$689$	−50354.8	−	87217.2i	−0.106073	−	0.183723i
$690$		0			0
$691$	289343.	+	167052.i	0.605978	+	0.349862i	0.771390	−	0.636363i	$-0.219562\pi$
$691$	289343.	+	167052.i	0.605978	+	0.349862i	−0.165411	+	0.986225i	$0.552895\pi$
$692$	−36678.4	+	30550.6i	−0.0765945	+	0.0637981i
$693$		0			0
$694$	184101.	+	508685.i	0.382241	+	1.05616i
$695$	214335.	+	123746.i	0.443734	+	0.256190i
$696$		0			0
$697$	−266302.	−	461249.i	−0.548162	−	0.949445i
$698$	10105.2	+	8510.57i	0.0207412	+	0.0174682i
$699$		0			0
$700$	−78246.8	+	13504.3i	−0.159687	+	0.0275599i
$701$	−177927.			−0.362082			−0.181041	−	0.983476i	$-0.557947\pi$
$701$	−177927.			−0.362082			−0.181041	+	0.983476i	$0.557947\pi$
$702$		0			0
$703$			40184.1i			0.0813100i
$704$	4839.78	−	444408.i	0.00976517	−	0.896679i
$705$		0			0
$706$	−130741.	−	110110.i	−0.262303	−	0.220911i
$707$	16252.4	−	9383.33i	0.0325146	−	0.0187723i
$708$		0			0
$709$	−362484.	+	627841.i	−0.721102	+	1.24899i	0.239456	+	0.970907i	$0.423031\pi$
$709$	−362484.	+	627841.i	−0.721102	+	1.24899i	−0.960558	+	0.278079i	$0.910302\pi$
$710$	172657.	+	477064.i	0.342506	+	0.946368i
$711$		0			0
$712$	−18067.3	+	30903.7i	−0.0356396	+	0.0609607i
$713$	−158298.	+	274180.i	−0.311383	+	0.539332i
$714$		0			0
$715$	237782.	−	137284.i	0.465122	−	0.268538i
$716$	−249810.	+	678672.i	−0.487286	+	1.32384i
$717$		0			0
$718$	−692358.	−	123378.i	−1.34302	−	0.239325i
$719$		−	536436.i		−	1.03767i	−0.854874	−	0.518836i	$-0.826366\pi$
$719$		−	536436.i		−	1.03767i	0.854874	−	0.518836i	$-0.173634\pi$
$720$		0			0
$721$	−252741.			−0.486189
$722$	65742.8	−	368929.i	0.126117	−	0.707731i
$723$		0			0
$724$	−414431.	−	152546.i	−0.790632	−	0.291021i
$725$	76751.2	+	132937.i	0.146019	+	0.252912i
$726$		0			0
$727$	375814.	+	216977.i	0.711057	+	0.410529i	0.811452	−	0.584418i	$-0.198677\pi$
$727$	375814.	+	216977.i	0.711057	+	0.410529i	−0.100395	+	0.994948i	$0.532011\pi$
$728$	125342.	+	73278.9i	0.236501	+	0.138266i
$729$		0			0
$730$	210178.	−	76066.7i	0.394403	−	0.142741i
$731$	1.45577e6	+	840486.i	2.72431	+	1.57288i
$732$		0			0
$733$	390208.	+	675860.i	0.726254	+	1.25791i	0.958456	+	0.285241i	$0.0920735\pi$
$733$	390208.	+	675860.i	0.726254	+	1.25791i	−0.232202	+	0.972667i	$0.574593\pi$
$734$	−20432.5	+	24260.9i	−0.0379253	+	0.0450314i
$735$		0			0
$736$	−344801.	+	921234.i	−0.636521	+	1.70065i
$737$	−767746.			−1.41346
$738$		0			0
$739$		−	215142.i		−	0.393947i	−0.980409	−	0.196973i	$-0.936889\pi$
$739$		−	215142.i		−	0.393947i	0.980409	−	0.196973i	$-0.0631112\pi$
$740$	16344.1	+	94700.9i	0.0298468	+	0.172938i
$741$		0			0
$742$	75250.1	−	89349.7i	0.136678	−	0.162288i
$743$	−250360.	+	144546.i	−0.453511	+	0.261835i	−0.709312	−	0.704895i	$-0.750994\pi$
$743$	−250360.	+	144546.i	−0.453511	+	0.261835i	0.255801	+	0.966730i	$0.417661\pi$
$744$		0			0
$745$	−181567.	+	314484.i	−0.327133	+	0.566612i
$746$	−927794.	+	335784.i	−1.66715	+	0.603367i
$747$		0			0
$748$	560178.	+	672537.i	1.00120	+	1.20202i
$749$	−10319.0	+	17873.0i	−0.0183939	+	0.0318592i
$750$		0			0
$751$	593117.	−	342436.i	1.05162	−	0.607156i	0.128521	−	0.991707i	$-0.458977\pi$
$751$	593117.	−	342436.i	1.05162	−	0.607156i	0.923104	+	0.384551i	$0.125644\pi$
$752$	−96822.4	−	272149.i	−0.171214	−	0.481250i
$753$		0			0
$754$	49241.5	−	276329.i	0.0866141	−	0.486052i
$755$		−	365213.i		−	0.640697i
$756$		0			0
$757$	−646906.			−1.12888			−0.564442	−	0.825472i	$-0.690909\pi$
$757$	−646906.			−1.12888			−0.564442	+	0.825472i	$0.690909\pi$
$758$	580545.	+	103452.i	1.01041	+	0.180054i
$759$		0			0
$760$	−1908.24	+	350455.i	−0.00330374	+	0.606744i
$761$	383411.	+	664087.i	0.662057	+	1.14672i	0.980074	+	0.198631i	$0.0636495\pi$
$761$	383411.	+	664087.i	0.662057	+	1.14672i	−0.318018	+	0.948085i	$0.603017\pi$
$762$		0			0
$763$	384828.	+	222181.i	0.661025	+	0.381643i
$764$	192745.	+	231405.i	0.330214	+	0.396448i
$765$		0			0
$766$	−166566.	−	460233.i	−0.283876	−	0.784369i
$767$	−357113.	−	206179.i	−0.607037	−	0.350473i
$768$		0			0
$769$	289867.	+	502065.i	0.490170	+	0.848999i	0.999936	−	0.0113137i	$-0.00360135\pi$
$769$	289867.	+	502065.i	0.490170	+	0.848999i	−0.509766	+	0.860313i	$0.670268\pi$
$770$	243596.	+	205156.i	0.410855	+	0.346021i
$771$		0			0
$772$	25726.4	+	149064.i	0.0431662	+	0.250114i
$773$	885783.			1.48241			0.741205	−	0.671279i	$-0.234255\pi$
$773$	885783.			1.48241			0.741205	+	0.671279i	$0.234255\pi$
$774$		0			0
$775$			63770.7i			0.106174i
$776$	69791.3	+	122417.i	0.115899	+	0.203291i
$777$		0			0
$778$	561285.	+	472713.i	0.927309	+	0.780977i
$779$	−175110.	+	101100.i	−0.288561	+	0.166601i
$780$		0			0
$781$	240523.	−	416598.i	0.394325	−	0.682991i
$782$	−659257.	−	1.82157e6i	−1.07806	−	2.97875i
$783$		0			0
$784$	80678.1	−	438892.i	0.131257	−	0.714045i
$785$	580281.	−	1.00508e6i	0.941671	−	1.63102i
$786$		0			0
$787$	−910515.	+	525686.i	−1.47007	+	0.848744i	−0.999436	−	0.0335849i	$-0.989308\pi$
$787$	−910515.	+	525686.i	−1.47007	+	0.848744i	−0.470633	+	0.882329i	$0.655974\pi$
$788$	−325077.	−	119657.i	−0.523521	−	0.192701i
$789$		0			0
$790$	−198246.	−	35327.3i	−0.317651	−	0.0566052i
$791$		−	439820.i		−	0.702946i
$792$		0			0
$793$	495287.			0.787609
$794$	57168.1	−	320811.i	0.0906803	−	0.508871i
$795$		0			0
$796$	−139616.	+	379303.i	−0.220348	+	0.598632i
$797$	−47409.2	−	82115.1i	−0.0746356	−	0.129273i	0.826292	−	0.563242i	$-0.190446\pi$
$797$	−47409.2	−	82115.1i	−0.0746356	−	0.129273i	−0.900928	+	0.433969i	$0.857113\pi$
$798$		0			0
$799$	492666.	+	284441.i	0.771719	+	0.445552i
$800$	32633.2	+	195426.i	0.0509894	+	0.305354i
$801$		0			0
$802$	756643.	−	273841.i	1.17636	−	0.425745i
$803$	−183538.	−	105966.i	−0.284640	−	0.164337i
$804$		0			0
$805$	−352436.	−	610436.i	−0.543861	−	0.941995i
$806$	75114.7	−	89189.0i	0.115626	−	0.137291i
$807$		0			0
$808$	−23192.7	−	40680.8i	−0.0355245	−	0.0623113i
$809$	209085.			0.319467			0.159734	−	0.987160i	$-0.448937\pi$
$809$	209085.			0.319467			0.159734	+	0.987160i	$0.448937\pi$
$810$		0			0
$811$		−	577209.i		−	0.877589i	−0.898587	−	0.438794i	$-0.855406\pi$
$811$		−	577209.i		−	0.877589i	0.898587	−	0.438794i	$-0.144594\pi$
$812$	320827.	−	55370.4i	0.486585	−	0.0839781i
$813$		0			0
$814$	58696.8	−	69694.9i	0.0885862	−	0.105185i
$815$	−170287.	+	98315.3i	−0.256370	+	0.148015i
$816$		0			0
$817$	319086.	−	552673.i	0.478039	−	0.827987i
$818$	528983.	−	191447.i	0.790560	−	0.286116i
$819$		0			0
$820$	−371558.	+	309483.i	−0.552585	+	0.460266i
$821$	−367923.	+	637262.i	−0.545847	+	0.945435i	0.452706	+	0.891660i	$0.350459\pi$
$821$	−367923.	+	637262.i	−0.545847	+	0.945435i	−0.998553	+	0.0537749i	$0.982875\pi$
$822$		0			0
$823$	−148172.	+	85547.4i	−0.218760	+	0.126301i	−0.605376	−	0.795940i	$-0.706977\pi$
$823$	−148172.	+	85547.4i	−0.218760	+	0.126301i	0.386616	+	0.922241i	$0.373644\pi$
$824$	−3433.88	+	630644.i	−0.00505743	+	0.928817i
$825$		0			0
$826$	83911.7	−	470888.i	0.122988	−	0.690172i
$827$			1.03882e6i			1.51890i	0.650563	+	0.759452i	$0.274533\pi$
$827$			1.03882e6i			1.51890i	−0.650563	+	0.759452i	$0.725467\pi$
$828$		0			0
$829$	−802150.			−1.16720			−0.583601	−	0.812040i	$-0.698357\pi$
$829$	−802150.			−1.16720			−0.583601	+	0.812040i	$0.698357\pi$
$830$	−341052.	−	60775.2i	−0.495068	−	0.0882206i
$831$		0			0
$832$	184550.	−	311760.i	0.266604	−	0.450374i
$833$	439420.	+	761098.i	0.633272	+	1.09686i
$834$		0			0
$835$	−869879.	−	502225.i	−1.24763	−	0.720320i
$836$	255325.	−	212668.i	0.365326	−	0.304292i
$837$		0			0
$838$	−209216.	−	578078.i	−0.297925	−	0.823187i
$839$	−487546.	−	281485.i	−0.692615	−	0.399881i	0.111976	−	0.993711i	$-0.464282\pi$
$839$	−487546.	−	281485.i	−0.692615	−	0.399881i	−0.804591	+	0.593830i	$0.797615\pi$
$840$		0			0
$841$	38945.5	+	67455.6i	0.0550637	+	0.0953732i
$842$	472424.	+	397874.i	0.666358	+	0.561205i
$843$		0			0
$844$	339980.	−	58676.0i	0.477275	−	0.0823713i
$845$	−593291.			−0.830910
$846$		0			0
$847$			73554.1i			0.102527i
$848$	−221925.	−	188979.i	−0.308613	−	0.262798i
$849$		0			0
$850$	−298458.	−	251360.i	−0.413090	−	0.347903i
$851$	−174651.	+	100835.i	−0.241164	+	0.139236i
$852$		0			0
$853$	331406.	−	574011.i	0.455472	−	0.788901i	−0.543243	−	0.839575i	$-0.682804\pi$
$853$	331406.	−	574011.i	0.455472	−	0.788901i	0.998715	+	0.0506745i	$0.0161371\pi$
$854$	195509.	+	540206.i	0.268072	+	0.740703i
$855$		0			0
$856$	44456.9	+	25991.0i	0.0606725	+	0.0354712i
$857$	566602.	−	981383.i	0.771465	−	1.33622i	−0.165294	−	0.986244i	$-0.552857\pi$
$857$	566602.	−	981383.i	0.771465	−	1.33622i	0.936760	−	0.349973i	$-0.113809\pi$
$858$		0			0
$859$	347489.	−	200623.i	0.470928	−	0.271890i	−0.245700	−	0.969346i	$-0.579018\pi$
$859$	347489.	−	200623.i	0.470928	−	0.271890i	0.716628	+	0.697456i	$0.245685\pi$
$860$	527193.	−	1.43225e6i	0.712808	−	1.93652i
$861$		0			0
$862$	754431.	+	134439.i	1.01532	+	0.180930i
$863$		−	1.22445e6i		−	1.64407i	−0.569437	−	0.822035i	$-0.692839\pi$
$863$		−	1.22445e6i		−	1.64407i	0.569437	−	0.822035i	$-0.307161\pi$
$864$		0			0
$865$	−85354.1			−0.114075
$866$	−37868.6	+	212508.i	−0.0504945	+	0.283360i
$867$		0			0
$868$	126928.	+	46720.7i	0.168469	+	0.0620111i
$869$	95465.2	+	165351.i	0.126417	+	0.218961i
$870$		0			0
$871$	−541994.	−	312920.i	−0.714427	−	0.412475i
$872$	559618.	−	957212.i	0.735967	−	1.25885i
$873$		0			0
$874$	−691550.	+	250283.i	−0.905317	+	0.327649i
$875$	274217.	+	158319.i	0.358161	+	0.206784i
$876$		0			0
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	0.819977	−	0.572397i	$-0.193986\pi$
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	−0.905698	+	0.423922i	$0.860653\pi$
$878$	43399.2	−	51530.9i	0.0562979	−	0.0668465i
$879$		0			0
$880$	515219.	−	605039.i	0.665314	−	0.781300i
$881$	−510450.			−0.657660			−0.328830	−	0.944389i	$-0.606654\pi$
$881$	−510450.			−0.657660			−0.328830	+	0.944389i	$0.606654\pi$
$882$		0			0
$883$		−	233561.i		−	0.299557i	−0.988720	−	0.149778i	$-0.952144\pi$
$883$		−	233561.i		−	0.299557i	0.988720	−	0.149778i	$-0.0478560\pi$
$884$	121346.	+	703100.i	0.155281	+	0.899730i
$885$		0			0
$886$	−416875.	+	494985.i	−0.531053	+	0.630557i
$887$	−554282.	+	320015.i	−0.704504	+	0.406746i	−0.809023	−	0.587777i	$-0.800003\pi$
$887$	−554282.	+	320015.i	−0.704504	+	0.406746i	0.104519	+	0.994523i	$0.466670\pi$
$888$		0			0
$889$	123005.	−	213050.i	0.155639	−	0.269574i
$890$	−60188.2	+	21783.1i	−0.0759856	+	0.0275004i
$891$		0			0
$892$	197576.	+	237205.i	0.248316	+	0.298122i
$893$	107986.	−	187038.i	0.135415	−	0.234545i
$894$		0			0
$895$	−1.11987e6	+	646558.i	−1.39805	+	0.807164i
$896$	412883.	+	78223.6i	0.514293	+	0.0974365i
$897$		0			0
$898$	−89261.5	+	500909.i	−0.110691	+	0.621164i
$899$		−	261472.i		−	0.323524i
$900$		0			0
$901$	574055.			0.707137
$902$	451386.	+	80436.5i	0.554798	+	0.0988645i
$903$		0			0
$904$	−1.09745e6	−	5975.64i	−1.34291	−	0.00731219i
$905$	−394820.	−	683849.i	−0.482061	−	0.834954i
$906$		0			0
$907$	−379256.	−	218964.i	−0.461018	−	0.266169i	0.251454	−	0.967869i	$-0.419091\pi$
$907$	−379256.	−	218964.i	−0.461018	−	0.266169i	−0.712472	+	0.701700i	$0.752425\pi$
$908$	663862.	+	797017.i	0.805204	+	0.966710i
$909$		0			0
$910$	88349.7	+	244116.i	0.106690	+	0.294791i
$911$	−666090.	−	384567.i	−0.802594	−	0.463378i	0.0417834	−	0.999127i	$-0.486696\pi$
$911$	−666090.	−	384567.i	−0.802594	−	0.463378i	−0.844377	+	0.535749i	$0.820029\pi$
$912$		0			0
$913$	164233.	+	284460.i	0.197024	+	0.341256i
$914$	−57665.1	−	48565.4i	−0.0690273	−	0.0581346i
$915$		0			0
$916$	106536.	+	617288.i	0.126971	+	0.735694i
$917$	−116490.			−0.138532
$918$		0			0
$919$		−	1.37883e6i		−	1.63260i	−0.577626	−	0.816301i	$-0.696021\pi$
$919$		−	1.37883e6i		−	1.63260i	0.577626	−	0.816301i	$-0.303979\pi$
$920$	−1.52796e6	+	871111.i	−1.80525	+	1.02920i
$921$		0			0
$922$	179507.	+	151180.i	0.211164	+	0.177841i
$923$	339597.	−	196066.i	0.398621	−	0.230144i
$924$		0			0
$925$	−20310.8	+	35179.3i	−0.0237380	+	0.0411153i
$926$	64709.1	+	178796.i	0.0754646	+	0.208514i
$927$		0			0
$928$	−133802.	−	801287.i	−0.155370	−	0.930448i
$929$	−130885.	+	226699.i	−0.151656	+	0.262675i	−0.931836	−	0.362879i	$-0.881794\pi$
$929$	−130885.	+	226699.i	−0.151656	+	0.262675i	0.780181	+	0.625554i	$0.215127\pi$
$930$		0			0
$931$	288946.	−	166823.i	0.333363	−	0.192467i
$932$	−34647.8	−	12753.4i	−0.0398881	−	0.0146823i
$933$		0			0
$934$	593394.	+	105742.i	0.680220	+	0.121215i
$935$			1.56506e6i			1.79022i
$936$		0			0
$937$	1.29656e6			1.47677			0.738384	−	0.674380i	$-0.235589\pi$
$937$	1.29656e6			1.47677			0.738384	+	0.674380i	$0.235589\pi$
$938$	127354.	−	714671.i	0.144746	−	0.812270i
$939$		0			0
$940$	178415.	−	484709.i	0.201918	−	0.548562i
$941$	−211160.	−	365741.i	−0.238470	−	0.413042i	0.721806	−	0.692096i	$-0.243312\pi$
$941$	−211160.	−	365741.i	−0.238470	−	0.413042i	−0.960275	+	0.279054i	$0.909979\pi$
$942$		0			0
$943$	−878816.	−	507385.i	−0.988267	−	0.570576i
$944$	−1.17383e6	−	215776.i	−1.31723	−	0.242136i
$945$		0			0
$946$	−1.36071e6	+	492462.i	−1.52048	+	0.550288i
$947$	844845.	+	487772.i	0.942057	+	0.543897i	0.890605	−	0.454779i	$-0.150282\pi$
$947$	844845.	+	487772.i	0.942057	+	0.543897i	0.0514525	+	0.998675i	$0.483615\pi$
$948$		0			0
$949$	−86379.8	−	149614.i	−0.0959135	−	0.166127i
$950$	−95427.4	+	113308.i	−0.105737	+	0.125549i
$951$		0			0
$952$	−718966.	+	409892.i	−0.793294	+	0.452267i
$953$	−1.52194e6			−1.67576			−0.837878	−	0.545857i	$-0.816204\pi$
$953$	−1.52194e6			−1.67576			−0.837878	+	0.545857i	$0.816204\pi$
$954$		0			0
$955$			538502.i			0.590447i
$956$	1.20159e6	−	207379.i	1.31475	−	0.226907i
$957$		0			0
$958$	142311.	−	168976.i	0.155062	−	0.184117i
$959$	108877.	−	62860.3i	0.118386	−	0.0683501i
$960$		0			0
$961$	−407448.	+	705720.i	−0.441190	+	0.764163i
$962$	69843.8	−	25277.6i	0.0754705	−	0.0273140i
$963$		0			0
$964$	200567.	−	167058.i	0.215826	−	0.179769i
$965$	−135239.	+	234241.i	−0.145227	+	0.251540i
$966$		0			0
$967$	−1.31627e6	+	759947.i	−1.40764	+	0.812700i	−0.995160	−	0.0982670i	$-0.968670\pi$
$967$	−1.31627e6	+	759947.i	−1.40764	+	0.812700i	−0.412478	+	0.910967i	$0.635337\pi$
$968$	183534.	+	999.347i	0.195869	+	0.00106651i
$969$		0			0
$970$	−44203.5	+	248057.i	−0.0469800	+	0.263638i
$971$			606895.i			0.643687i	0.946793	+	0.321844i	$0.104303\pi$
$971$			606895.i			0.643687i	−0.946793	+	0.321844i	$0.895697\pi$
$972$		0			0
$973$	221881.			0.234366
$974$	−11717.7	−	2088.09i	−0.0123517	−	0.00220106i
$975$		0			0
$976$	1.35059e6	−	480499.i	1.41783	−	0.504421i
$977$	−440254.	−	762542.i	−0.461226	−	0.798867i	0.537796	−	0.843075i	$-0.319257\pi$
$977$	−440254.	−	762542.i	−0.461226	−	0.798867i	−0.999022	+	0.0442080i	$0.985924\pi$
$978$		0			0
$979$	52559.6	+	30345.3i	0.0548386	+	0.0316611i
$980$	613101.	−	510672.i	0.638381	−	0.531728i
$981$		0			0
$982$	368508.	+	1.01821e6i	0.382141	+	1.05588i
$983$	−1.55074e6	−	895318.i	−1.60484	−	0.926553i	−0.990501	−	0.137509i	$-0.956091\pi$
$983$	−1.55074e6	−	895318.i	−1.60484	−	0.926553i	−0.614336	−	0.789044i	$-0.710576\pi$
$984$		0			0
$985$	−309695.	−	536407.i	−0.319199	−	0.552869i
$986$	1.22374e6	+	1.03063e6i	1.25873	+	1.06010i
$987$		0			0
$988$	266928.	−	46068.1i	0.273451	−	0.0471940i
$989$	3.20275e6			3.27439
$990$		0			0
$991$			1.12180e6i			1.14227i	0.820858	+	0.571133i	$0.193496\pi$
$991$			1.12180e6i			1.14227i	−0.820858	+	0.571133i	$0.806504\pi$
$992$	118303.	−	316080.i	0.120219	−	0.321198i
$993$		0			0
$994$	347900.	+	293001.i	0.352113	+	0.296549i
$995$	−625885.	+	361355.i	−0.632191	+	0.364996i
$996$		0			0
$997$	−420584.	+	728473.i	−0.423119	+	0.732864i	−0.996243	−	0.0866051i	$-0.972398\pi$
$997$	−420584.	+	728473.i	−0.423119	+	0.732864i	0.573124	+	0.819469i	$0.305731\pi$
$998$	355769.	+	983016.i	0.357197	+	0.986960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.f.a.19.13		44
3.2	odd	2		36.5.f.a.7.10	yes	44
4.3	odd	2	inner	108.5.f.a.19.18		44
9.2	odd	6		324.5.d.f.163.19		22
9.4	even	3	inner	108.5.f.a.91.18		44
9.5	odd	6		36.5.f.a.31.5	yes	44
9.7	even	3		324.5.d.e.163.4		22
12.11	even	2		36.5.f.a.7.5	✓	44
36.7	odd	6		324.5.d.e.163.3		22
36.11	even	6		324.5.d.f.163.20		22
36.23	even	6		36.5.f.a.31.10	yes	44
36.31	odd	6	inner	108.5.f.a.91.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.5	✓	44	12.11	even	2
36.5.f.a.7.10	yes	44	3.2	odd	2
36.5.f.a.31.5	yes	44	9.5	odd	6
36.5.f.a.31.10	yes	44	36.23	even	6
108.5.f.a.19.13		44	1.1	even	1	trivial
108.5.f.a.19.18		44	4.3	odd	2	inner
108.5.f.a.91.13		44	36.31	odd	6	inner
108.5.f.a.91.18		44	9.4	even	3	inner
324.5.d.e.163.3		22	36.7	odd	6
324.5.d.e.163.4		22	9.7	even	3
324.5.d.f.163.19		22	9.2	odd	6
324.5.d.f.163.20		22	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.701741 - 3.93796i) q^{2} +(-15.0151 - 5.52686i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(-22.2124 - 12.8243i) q^{7} +(-32.3013 + 55.2506i) q^{8} +O(q^{10})\)	\(q+(0.701741 - 3.93796i) q^{2} +(-15.0151 - 5.52686i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(-22.2124 - 12.8243i) q^{7} +(-32.3013 + 55.2506i) q^{8} +(-107.606 + 38.9445i) q^{10} +(93.9677 + 54.2523i) q^{11} +(44.2246 + 76.5993i) q^{13} +(-66.0891 + 78.4722i) q^{14} +(194.908 + 165.973i) q^{16} -504.169 q^{17} +191.405i q^{19} +(77.8502 + 451.079i) q^{20} +(279.585 - 331.970i) q^{22} +(-831.897 + 480.296i) q^{23} +(-96.7443 + 167.566i) q^{25} +(332.680 - 120.402i) q^{26} +(262.643 + 315.324i) q^{28} +(396.671 - 687.053i) q^{29} +(285.428 - 164.792i) q^{31} +(790.370 - 651.069i) q^{32} +(-353.796 + 1985.40i) q^{34} +733.789i q^{35} +209.943 q^{37} +(753.745 + 134.317i) q^{38} +(1830.96 + 9.96965i) q^{40} +(528.200 + 914.869i) q^{41} +(-2887.45 - 1667.07i) q^{43} +(-1111.09 - 1333.95i) q^{44} +(1307.61 + 3613.02i) q^{46} +(-977.185 - 564.178i) q^{47} +(-871.573 - 1509.61i) q^{49} +(591.979 + 498.563i) q^{50} +(-240.684 - 1394.57i) q^{52} -1138.62 q^{53} -3104.23i q^{55} +(1426.04 - 813.005i) q^{56} +(-2427.23 - 2044.21i) q^{58} +(-4037.49 + 2331.05i) q^{59} +(2799.84 - 4849.46i) q^{61} +(-448.648 - 1239.65i) q^{62} +(-2009.25 - 3569.33i) q^{64} +(1265.23 - 2191.45i) q^{65} +(-6127.74 + 3537.85i) q^{67} +(7570.16 + 2786.47i) q^{68} +(2889.63 + 514.930i) q^{70} -4433.42i q^{71} -1953.21 q^{73} +(147.326 - 826.748i) q^{74} +(1057.87 - 2873.97i) q^{76} +(-1391.50 - 2410.15i) q^{77} +(1523.90 + 879.826i) q^{79} +(1324.12 - 7203.27i) q^{80} +(3973.38 - 1438.03i) q^{82} +(2621.64 + 1513.61i) q^{83} +(7211.95 + 12491.5i) q^{85} +(-8591.12 + 10200.8i) q^{86} +(-6032.75 + 3439.35i) q^{88} +559.336 q^{89} -2268.61i q^{91} +(15145.6 - 2613.92i) q^{92} +(-2907.44 + 3452.21i) q^{94} +(4742.31 - 2737.97i) q^{95} +(1100.89 - 1906.79i) q^{97} +(-6556.40 + 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8}+O(q^{10}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8	\( 44 q + q^{2} - q^{4} + 2 q^{5} - 122 q^{8} + 28 q^{10} - 2 q^{13} - 252 q^{14} - q^{16} + 56 q^{17} + 140 q^{20} - 33 q^{22} - 1752 q^{25} - 1096 q^{26} - 516 q^{28} - 526 q^{29} + 121 q^{32} + 385 q^{34} - 8 q^{37} - 1395 q^{38} - 2276 q^{40} + 2762 q^{41} - 6714 q^{44} + 3576 q^{46} + 3428 q^{49} - 6375 q^{50} + 1438 q^{52} + 10088 q^{53} + 7506 q^{56} - 4064 q^{58} - 2 q^{61} + 18324 q^{62} + 9026 q^{64} + 2014 q^{65} + 11405 q^{68} + 3666 q^{70} - 3416 q^{73} - 14620 q^{74} + 1581 q^{76} + 3942 q^{77} - 45520 q^{80} - 8486 q^{82} - 1252 q^{85} - 22113 q^{86} + 1995 q^{88} - 13048 q^{89} + 30294 q^{92} + 7524 q^{94} + 5638 q^{97} + 92938 q^{98}+O(q^{100}) \) 44 * q + q^2 - q^4 + 2 * q^5 - 122 * q^8 + 28 * q^10 - 2 * q^13 - 252 * q^14 - q^16 + 56 * q^17 + 140 * q^20 - 33 * q^22 - 1752 * q^25 - 1096 * q^26 - 516 * q^28 - 526 * q^29 + 121 * q^32 + 385 * q^34 - 8 * q^37 - 1395 * q^38 - 2276 * q^40 + 2762 * q^41 - 6714 * q^44 + 3576 * q^46 + 3428 * q^49 - 6375 * q^50 + 1438 * q^52 + 10088 * q^53 + 7506 * q^56 - 4064 * q^58 - 2 * q^61 + 18324 * q^62 + 9026 * q^64 + 2014 * q^65 + 11405 * q^68 + 3666 * q^70 - 3416 * q^73 - 14620 * q^74 + 1581 * q^76 + 3942 * q^77 - 45520 * q^80 - 8486 * q^82 - 1252 * q^85 - 22113 * q^86 + 1995 * q^88 - 13048 * q^89 + 30294 * q^92 + 7524 * q^94 + 5638 * q^97 + 92938 * q^98

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